Quiet Sun Magnetic Fields Research Articles

The Distribution of Quiet Sun Magnetic Field Strengths from 0 to 1800 G

The quiet-Sun photospheric plasma has a variety of magnetic field strengths going from zero to 1800 G. The empirical characterization of these field strengths requires a probability density function (PDF), i.e., a function P(B) describing the fraction of quiet Sun occupied by each field strength B. We show how to combine magnetic field strength measurements based on the Zeeman effect and the Hanle effect to estimate an unbiased P(B). The application of the method to real observations renders a set of possible PDFs, which outline the general characteristics of the quiet-Sun magnetic fields. Their most probable field strength differs from zero. The magnetic energy density is a significant fraction of the kinetic energy of the granular motions at the base of the photosphere (larger than 15% or larger than 2 × 103 ergs cm-3). The unsigned flux density (or mean magnetic field strength) has to be between 130 and 190 G. A significant part of the unsigned flux (between 10% and 50%) and of the magnetic energy (between 45% and 85%) are provided by the field strengths larger than 500 G, which, however, occupy only a small fraction of the surface (between 1% and 10%). The fraction of kG fields in the quiet Sun is even smaller, but they are important for a number of reasons. The kG fields still trace a significant fraction of the total magnetic energy, they reach the high photosphere, and they appear in unpolarized light images. The quiet-Sun photosphere has far more unsigned magnetic flux and magnetic energy than the active regions and the network combined.

Domain structures in complex 3D magnetic fields

The numerous magnetic fragments that populate the mixed-polarity, quiet-Sun photosphere give rise to many interesting topological features in the corona. In light of this, much recent work has gone into classifying the configurations that arise from simple, point-source potential-field models in efforts to determine the nature of the quiet-Sun magnetic field. These studies have ranged from systematic and detailed examinations of magnetic fields arising from only a handful of sources, involving classifying the configurations that arise (and how some states may bifurcate into other states), to statistical studies of the overall properties of fields arising from hundreds of magnetic sources. Such studies have greatly increased our understanding of what we might expect the magnetic field over the quiet Sun to behave like; the purpose of the study presented here is to extend this understanding further by examining the structure of the individual domains (the regions in space through which pairs of opposite-polarity sources are connected). In particular, the features of lesser-known domain structures that are absent from fields arising from only a few sources and overlooked by sweeping statistical studies are documented. In spite of the incredible complexity of the coronal field, previous studies have shown that there are only two types of building block in a potential field arising from coplanar point sources: namely, an isolated dome, bounded by a single unbroken separatrix surface, and a separator-ring domain, engirdled by a ring of separators. However, it is demonstrated here how both isolated domains and separator-ring domains may be categorised further depending upon their particular geometrical and topological traits. As many models predict coronal heating at topologically distinct features in magnetic fields such as null points, separators and separatrices, for any such models to be applied to general fields would require a scheme for identifying which topological features are related to a given domain. The study here explores some of the issues that would need to be taken into account by such a scheme, and in particular the problems associated with trying to deduce the properties of a general magnetic field from knowledge of domain footprints alone. Animated 3D-rotational views of some of the figures in this manuscript may be viewed in AVI, MPEG and animated-GIF formats by visiting http://www-solar.mcs.st-and.ac.uk/robertc/animations/blocks.html and following the desired link.

Quiet sun magnetic fields vs. polar faculae – local vs. global dynamo?

AbstractQuiet Sun magnetic fields in the internetwork are almost ubiquitous. Simultaneous observations in infra‐red and visible lines and high spatial resolution (<0.5″) data in visible lines show that their field strengths range from below few hundred Gauss to kilo‐Gauss. Most of the flux is contained in small‐scale, strong‐field features located mainly in intergranular lanes. The average unsigned flux density exceeds 20 Gauss. The new detections are confirmed by recent quiet Sun observations in the G band. The generation of the strong fields in the internetwork, which may be due to a local dynamo, poses a challenging problem. – Polar faculae (PFe) are small‐scale magnetic features at the polar caps of the Sun. They take part in the solar cycle and are thus likely to be rooted deeply in the solar interior. They are the result of the global dynamo at the solar poles. PFe also possess kilo‐Gauss magnetic fields which have the same polarity as the global magnetic field. The rôle of quiet Sun magnetic field structures and of PFe for the dynamics of the corona and for the solar wind are addressed. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Effects of Complexity on the Flux-Tube Tectonics Model

The quiet-Sun magnetic field emerges through the solar photosphere in a multitude of mixed-polarity magnetic concentrations and is subsequently tangled up into intricate regions of interconnecting flux. Moreover, since these discrete concentrations are likely to be extremely small in size, with fluxes of around only 1017 Mx, the number of such flux sources in, say, a supergranule, will be extremely large. The flux-tube tectonics model of Priest, Heyvaerts, and Title (2002) demonstrated how the formation and dissipation of current sheets along the separatrices that separate the regions of different connectivity are likely to make an important contribution to coronal heating. Since the full complexity of the magnetic field is below present observable scales, this study examines the effect of having the magnetic flux emerge through configurations structured on smaller and smaller scales. It is found that, by fixing the amount of flux emerging into a given 2D region, the main factors influencing the current build-up along the separatrices are the number of sources through which the flux emerges and the spatial distribution of the sources on the photosphere. The free energy (i.e., that above potential) is stored lower and lower in the atmosphere as the complexity of the system increases. A simple comparison is then made between coronal heating by separator currents and by separatrix currents. It is found that both result in comparable amounts of energy release, with separatrix heating being the more dominant.

Local Modulation of Solar Oscillations by Magnetic Fields

The amplitudes of solar oscillations measured in Doppler velocity are modulated by the presence of a strong photospheric magnetic field. Here we show that the amount of modulation cannot be predicted solely on the local photospheric magnetic field strength. Qualitatively, magnetic fields of similar strength have similar effects on the oscillations. Quantitatively, however, we find a ‘neighborhood effect’, so that the presence of a nearby sunspot affects oscillations in the area in its vicinity that has normal quiet-Sun magnetic field strength. Thus, different types of magnetic regions alter the oscillatory power to a varying degree, and the p-mode power within regions of similar magnetic field strength is more reduced if there is a sunspot present. The neighborhood effect falls off with distance from the sunspot. We also show that our measurements of the power modulation, in which we look at the effects on oscillations pixel by pixel, can be made consistent with results of amplitude modulation of modes as obtained from ring-diagram analysis of active regions, but only if the neighborhood effect on quiet-Sun regions is taken into account.

Quiet-Sun inter-network magnetic fields observed in the infrared

This paper presents the results of an investigation of the quiet Sun's magnetic field based on high-resolution infrared spectropolarimetric observations obtained with the Tenerife Infrared Polarimeter (TIP) at the German VTT of the Observatorio del Teide. We observed two very quiet regions at disc centre. The seeing was exceptionally good during both observing runs, being excellent during one of them. In both cases the network was intentionally avoided to the extent possible, to focus the analysis on the characteristics of the weak polarization signals of the inter-network regions. We find that the Stokes V profile of Fe  15648 A line in almost 50% of the pixels and Stokes Q and/or U in 20% of the pixels have a signal above 10 −3 (in units of continuum intensity Ic), which is significantly above the noise level of 2−3 × 10 −4 . This implies that we detect fluxes as low as 2 × 10 15 Mx/px. We find evidence that we have detected most of the net flux that is in principle detectable at 1 �� resolution with the Zeeman effect. The observed linear polarization resulting from the transverse Zeeman effect indicates that the magnetic fields have a broad range of inclinations, although most of the pixels show polarization signatures which imply an inclination of about 20 ◦ . Nearly 30% of the selected V-profiles have irregular shapes with 3 or more lobes, suggesting mixed polarities with different LOS velocity within the resolution element. The profiles are classified using a single value decomposition approach. The spatial distribution of the magnetic signal shows that profiles of different classes (having different velocities, splitting, asymmetries) are clustered together and form patches, close to the spatial resolution in size. Most of the field is found to be located in intergranular lanes. The statistical properties of the mainly inter-network field sampled by these observations are presented, showing that most of the observed fields are weak with relatively few kG features. The field strength distribution peaks at 350 G and has a FWHM of 300 G. Other parameters, such as profile asymmetries, filling factors and line-of-sight velocities are also determined and discussed.

Magnetic Helicity Injection by Horizontal Flows in the Quiet Sun. I. Mutual‐Helicity Flux

The flux of magnetic helicity through the solar photosphere has implications in diverse areas of current solar research, including solar dynamo modeling and coronal heating. In this work, we focus on the flux of magnetic helicity from quiet-Sun magnetic fields. We express the total helicity flux in terms of mutual and self-helicities, which arise from relative motions of separate flux elements and from internal motions within individual magnetic flux elements, respectively. Using a novel labeling algorithm and a tracking algorithm applied to high-cadence, high-resolution Solar and Heliospheric Observatory Michelson Doppler Imager magnetograms, we determine the observed mutual-helicity flux density in the quiet Sun to be ~5 × 1012 Mx2 cm-2 s-1 and compare this value with a simple theoretical prediction. The observed rate corresponds to a whole-cycle, hemispheric mutual-helicity flux of ~1043 Mx2 from the quiet Sun, meaning that helicity injection by surface motions in quiet-Sun fields is negligible compared to the active region helicity flux rate.

Quiet-Sun Magnetic Fields at High Spatial Resolution

We present spectro-polarimetric observations of Inter-Network magnetic fields at the solar disk center. A Fabry-Perot spectrometer was used to scan the two Fe I lines at 6301.5 A and 6302.5 A. High spatial resolution (0.5) magnetograms were obtained after speckle reconstruction. The patches with magnetic fields above noise cover approximately 45% of the observed area. Such large coverage renders a mean unsigned magnetic flux density of some 20 G (or 20 Mx/cm^2), which exceeds all previous measurements. Magnetic signals occur predominantly in intergranular spaces. The systematic difference between the flux densities measured in the two iron lines leads to the conclusion that, typically, we detect structures with intrinsic field strengths larger than 1kG occupying only 2% of the surface.

Ephemeral Regions on a Sequence of Full‐Disk Michelson Doppler Imager Magnetograms

Ephemeral regions are small-scale, bipolar regions of magnetic field, emerging all over the solar surface. As structures ephemeral regions are short-lived; they can be recognized for 4.4 hr on average. This paper examines a 3.5 day sequence of full-disk Michelson Doppler Imager (MDI) magnetograms in order to estimate the importance of ephemeral regions to the total magnetic flux budget on the sun. The data were taken in 1997 October, which was around the minimum of solar cycle 22, and early in cycle 23. An algorithm was developed to automatically recognize ephemeral regions on this sequence of magnetograms. Assuming uniform emergence over the entire solar surface, the total amount of flux emerging in ephemeral regions is estimated to be 5 × 1023 Mx-1. This rate of emergence is sufficient to replace the magnetic field in quiet sun in 14 hr. In total, 38,000 ephemeral regions are found, with an absolute flux Φ in the range (2.6-407) × 1018 Mx. The distribution function of their fluxes follows an exponential with an average of 11.3 × 1018 Mx. This relatively low flux content may be due to the fact that these ephemeral regions are detected before they have reached a maximum. After their first recognition, they increase in flux with a rate of typically dΦ/dt = 1.6 × 1015 Mx s-1. Only 60% of the ephemeral regions are found to have the orientation expected in cycle 22. After emergence, the outer borders of the ephemeral regions expand from a size of 8.9 Mm, with a velocity of 2.3 km s-1. No particular pattern can be recognized from a map of all locations of flux emergence. From a χ2 test it is found that the emergences occur randomly, on a scale below 20 Mm. On larger scales some order is found, but its origin remains unknown.

Soft X‐Ray Luminosity and Photospheric Magnetic Field in Quiet Sun

We use full-disk soft X-ray data from Yohkoh and Kitt Peak daily magnetograms to study the coronal irradiance and photospheric field remote from active regions between 1991 November and 1998 December. For every image of our data set we extract three areas 4° × 4° in size centered at N00° W00°, N50° W00°, and S50° W00° and compute X-ray irradiance and unsigned flux for each of these areas. Between 1991 (active Sun) and 1996 (quiet Sun) the X-ray irradiance at the heliographic center decreased by more than a factor of 7, while the flux decreased by only a factor of 2. A similar tendency is observed for our high-latitude samples. Apart from the cycle-related variations, all three areas of quiet Sun exhibit significant nonperiodic changes in X-ray irradiance. These variations occur on 9-12 month intervals and clearly correlate with changes in sunspot activity. Similar variations are present in the total X-ray irradiance averaged over the solar disk. By contrast, the fluxes from the photosphere beneath these same areas show no corresponding variations on this time scale. In our opinion, coronal heating models based on the reconnection of quiet-Sun elements (variously called chromospheric network, magnetic carpet, or salt and pepper field) can at best account for a minimal contribution to heating the million-degree corona observed by the Yohkoh soft X-ray telescope. We conclude that the X-ray irradiance in the quiet Sun (at least in the Yohkoh temperature range, >2 MK) is primarily associated with the strong fields of active regions, not with weak photospheric fields. The association, however, is not direct. We interpret the enhanced X-ray irradiance above the quiet Sun not as a result of the coronal canopy formed by the active-region field above the quiet-Sun areas, but as the large-scale relaxation process in the corona triggered by the evolution of active regions. To further support this conclusion, we show examples of active and quiet hemispheres in 1996 with similar weak-field properties but greatly different global X-ray emission and a pronounced change in X-ray irradiance over the entire visible hemisphere that was associated with the emergence of a single small active region.

SUMER Observations of the Quiet Solar Atmosphere: The Network Chromosphere and Lower Transition Region

We examine spectral properties of the network chromosphere and lower transition region from the SUMER instrument on the SOHO spacecraft, using time-series data sets discussed in an accompanying Letter by Carlsson, Judge, & Wilhelm. The data were obtained early in the mission with no tracking of solar features and so cannot generally be used to examine intrinsic variations in features on timescales in excess of 383 s. Upon examination of the temporal variations and some preliminary power spectrum analysis, we find the following: (1) Transition region lines show more redshift in network regions than in internetwork regions and also a correlation between line intensity brightenings and increased redshift. (2) The internetwork "Ca II grain" phenomenon is not seen in He I λ584 or in lines of Si III and C III. (3) Very rapid changes are seen in the network for transition region lines with no obvious correspondence with the underlying chromosphere. (4) He I λ584 line profiles show very slow time variations. (5) Small-amplitude (2-5 km s−1) coherent oscillations of 5''-10'' scale length and ~130 s period are seen in Doppler shifts of Si III between regions of bright network elements. (6) Essentially all blueshifts or redshifts are substantially less than line widths. We conclude that upward-propagating acoustic shock waves do not contribute significantly to the heating of the lower transition region, and that ionization equilibrium is likely to fail for the interpretation of certain emission lines. The spatial coherency of the Si III velocity oscillations indicates that the quiet Sun's magnetic field topology is more uniform than emission-line intensity data alone might suggest.

The correspondence between x-ray bright points and evolving magnetic features in the quiet sun

Coronal bright points, first identified as X-ray Bright Points (XBPs), are compact, short-lived and associated with small-scale, opposite polarity magnetic flux features. Previous studies have yielded contradictory results suggesting that XBPs are either primarily a signature of emerging flux in the quiet Sun, or of the disappearance of pre-existing flux. With the goal of improving our understanding of the evolution of the quiet Sun magnetic field, we present results of a study of more recent data on XBPs and small-scale evolving magnetic structures. The coordinated data set consists of X-ray images obtained during rocket flights on 15 August and 11 December, 1987, full-disk magnetograms obtained at the National Solar Observatory - Kitt Peak, and time-lapse magnetograms of multiple fields obtained at Big Bear Solar Observatory. We find that XBPs were more frequently associated with pre-existing magnetic features of opposite polarity which appeared to be cancelling than with emerging or new flux regions. Most young, emerging regions were not associated with XBPs. However, some XBPs were associated with older ephemeral regions, some of which were cancelling with existing network or intranetwork poles. Nearly all of the XBPs corresponded to opposite polarity magnetic features which wereconverging towards each other; some of these had not yet begun cancelling. We suggest that most XBPs form when converging flow brings oppositely directed field lines together, leading to reconnection and heating of the newly-formed loops in the low corona.

Heights of formation of non-magnetic solar lines suitable for velocity studies

Heights of formation of lines that do not exhibit Zeeman splitting are calculated using an LTE, partial non-LTE, and full non-LTE approach. Non-magnetic (g=0) lines are valuable for velocity investigations in quiet-Sun magnetic field regions, and a knowledge of their formation heights is useful for obtaining three dimensional velocity profiles in these regions.